I think the wording in the AE Conan is not as clear as it should be. And explains why you are confused. It implies that if anyone flanks the target then you get sneak attack even if it is not you.
My bad. Sorry to have caused the confusion.
"Being flanked does not render you unable to dodge or parry, though you may still be sneak attacked if you are flanked." - This comment explains the dangers faced by a person who is flanked. They can be sneak attacked by one of the people doing the flanking.
"Only characters with levels in certain classes, such as thief or pirate, or from certain races, such as Zingaran, can make sneak attacks. A sneak attack can only be made against a character who is unable to use Dodge Defence or Parry Defence to defend himself, or who is being flanked." This should read "being flanked by the sneak attacker.
(Note to self: never, ever use the passive voice. 'Or who the attacker is flanking' would have been wholly unambiguous.)
Essentially, the flanking condition for sneak attacks is the 3.X revision of the old Thief ability to 'backstab'. There is no facing in d20 (nor in Conan), so counters don't have any 'back' to stab. Flanking is what replaces that. It establishes a stabbable 'back' relative to the attacker
rather than an absolute one. This is also why creatures with no discernible front or back, such as oozes, can't be flanked in d20.
Please note that this isn't an authoritative Mongoose statement, but since it was me who edited the AE and caused the confusion, I do feel I ought to speak up here!
Incidentally, if you want to play Conan in true authentic hardcore style, you should really refer to a 'round the corner stabby bonus' instead of a Flanking bonus. (This being what Ian Sturrock did when he couldn't remember the word 'flank' in a Conan game.)